Results (b) and (c) follow by Theorem 3.1 of [1]}, if, for any \(\epsilon >0\) ,
\(\liminf _{n \rightarrow \infty } \inf _{\theta \in B_\epsilon \left( \hat{\theta }_{TW}\right)^c} \left\lbrace  \ell _{TW}(\theta ; \mathbf {y}) - \ell _{TW}(\hat{\theta }_{TW}; \mathbf {y}) \right\rbrace  > 0,\) 
